**Table of Contents**

** Unit 1 | Algebra**

Page 1 | Expressions and Formulae

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

** Unit 2 |Graphs**

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

** Unit 3 |Geometry and Measure **

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

**Unit 4 | Numbers**

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

** Unit 5 | Statistics and Probability **

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

**Unit 4 | Calculus **

*Powers and Roots*

L.O – To learn and be able to apply the rules regarding powers and roots

__Powers__

Powers are the mini numbers on top of ‘normal’ numbers. They are a very useful shorthand e.g. 3^{4} is just a shorter way of writing 3x3x3x3 – the power tells us how many times to multiply 3 by itself.

**1. When multiplying, add the powers**

**Example 1:**

4^{2} + 4^{6 }= 4^{2+6} = 4^{8}

30^{3} + 30^{7} = 30^{3+7} = 30^{10}

**2. When dividing, subtract the powers**

**Example 1:**

6^{5} 6^{2} = 6^{5-2} = 6^{3}

15^{8} – 15^{5} = 15^{8-5} = 15^{3}

**3. When raising one power to another, multiply the powers**

** Example 1:**

(7^{2})^{4} = 7^{2×4 }= 7^{8}

(2^{5})^{3} = 2^{5×3 }= 2^{15}

**4. Anything to the power 1 is just itself**

**Example 1:**

X^{1} = X

5^{1} = 5

12^{1} = 12

**5. Anything to the power 0 is always 1**

**Example 1:**

X^{0 }= 1

3^{0 }= 1

29^{0} = 1

**6. 1 to any power is always 1 **

**Example 1:**

1^{2 }= 1

1^{24} = 1

1^{0} = 1

**7. With fractions, apply power to top and bottom**

**Example 1:**

*The numerator(1) and the denominator(3) of the fractions have been squared*

__Negative powers__

If a number/fraction is raised to a negative power;

**Turn the number/fraction upside down****Then make the power positive**

**Example 1:**

__Fractional powers__

The power means square root – √

The power means cubed root – ^{3}√

The power means fourth root – ^{4}√ etc.

**Example 1:**

25^{1/2} = √25 = 5

9^{1/3} = ^{3}√9 = 9

81^{1/4} = ^{4}√81 = 3

__Two stage fractional powers__

Some powers can be fractions like etc

These fractions represent a root and and a power

- The trick is to split the fraction into its root and power

- Once you have split the fraction,
**apply the root first, then the power**

**Example 1:**

9^{4/3}

– 9^{4/3} = (9)^{1/3 x 4} = (9^{1/3})^{4 }= 3^{4} = 81

125^{3/2}

– 125^{3/2} = (125)^{1/2 x 3} = (125^{1/2})^{3} = 25^{3} = 15625

__Square roots__

**The square root of a number can be positive or negative.** There is the possibility of a negative answer as when you square a negative number, the answer is positive.

**Example 1:**

√ 4 = +2 or -2

√64 = +8 or -8

**Questions:**